tests/perf_bench: Add bm_fft test.

This is mostly a test of complex number performance.

The FFT implementation is from Project Nayuki and is MIT licensed.

tests/perf_bench/bm_fft.py

@@ -0,0 +1,69 @@
+# Copyright (c) 2019 Project Nayuki. (MIT License)
+# https://www.nayuki.io/page/free-small-fft-in-multiple-languages
+
+import math, cmath
+
+def transform_radix2(vector, inverse):
+    # Returns the integer whose value is the reverse of the lowest 'bits' bits of the integer 'x'.
+    def reverse(x, bits):
+        y = 0
+        for i in range(bits):
+            y = (y << 1) | (x & 1)
+            x >>= 1
+        return y
+
+    # Initialization
+    n = len(vector)
+    levels = int(math.log2(n))
+    coef = (2 if inverse else -2) * cmath.pi / n
+    exptable = [cmath.rect(1, i * coef) for i in range(n // 2)]
+    vector = [vector[reverse(i, levels)] for i in range(n)]  # Copy with bit-reversed permutation
+
+    # Radix-2 decimation-in-time FFT
+    size = 2
+    while size <= n:
+        halfsize = size // 2
+        tablestep = n // size
+        for i in range(0, n, size):
+            k = 0
+            for j in range(i, i + halfsize):
+                temp = vector[j + halfsize] * exptable[k]
+                vector[j + halfsize] = vector[j] - temp
+                vector[j] += temp
+                k += tablestep
+        size *= 2
+    return vector
+
+###########################################################################
+# Benchmark interface
+
+bm_params = {
+    (50, 25): (2, 128),
+    (100, 100): (3, 256),
+    (1000, 1000): (20, 512),
+    (5000, 1000): (100, 512),
+}
+
+def bm_setup(params):
+    state = None
+    signal = [math.cos(2 * math.pi * i / params[1]) + 0j for i in range(params[1])]
+    fft = None
+    fft_inv = None
+
+    def run():
+        nonlocal fft, fft_inv
+        for _ in range(params[0]):
+            fft = transform_radix2(signal, False)
+            fft_inv = transform_radix2(fft, True)
+
+    def result():
+        nonlocal fft, fft_inv
+        fft[1] -= 0.5 * params[1]
+        fft[-1] -= 0.5 * params[1]
+        fft_ok = all(abs(f) < 1e-3 for f in fft)
+        for i in range(len(fft_inv)):
+            fft_inv[i] -= params[1] * signal[i]
+        fft_inv_ok = all(abs(f) < 1e-3 for f in fft_inv)
+        return params[0] * params[1], (fft_ok, fft_inv_ok)
+
+    return run, result